Do algorithms like OpenAI's "think up strategies"?
The key here is think up strategies. If we define this as examining, creating a hypothesis, and testing it as strategizing then yes AI has the ability to strategize. It can examine other users' games, quantifies actions that correlated with victory then test if it gains victory by doing those actions.

Strategy by definition is: a plan of action or policy designed to achieve a major or overall aim.

AI can not classically plan a series of actions designed to achieve a major victory. Instead, it learns the right strategy by testing simulated scenarios, like someone who thinks about the consequences before doing them, but the AI actually has the opportunity to play the game hundreds of times, in order to learn the correct strategy. Similar to Bill Murray in the movie Groundhog Day, learning the ideal day to live. The AI can strategize by experiencing the game over and over until it fine-tunes what an ideal game should be and has seen enough examples of games to not be outwitted by gimmicky strategies.

To summarize, AI can strategize, just in a way fairly different than people.